Field of the Disclosure
The present disclosure relates to methods and apparatus for measuring linear acceleration, and more specifically relates to methods and apparatus for measuring a local acceleration of gravity.
Description of the Related Art
Since the beginning of human civilization, many theories, hypotheses, and experiments were proposed to understand the dynamics of falling objects. The Greek philosopher Aristotle suggested that objects fall at speeds proportional to their masses. Aristotle's incorrect theory was discredited by Galileo's landmark experiment, where according to legend, Galileo chopped balls of different densities and masses from the tower of Pisa. Galileo noticed that if released simultaneously from rest, all objects tend to land at the same time, concluding that time of fall is independent of the mass of the object.
In the last few decades, and as a result of many advancements in science and technology, many techniques have been proposed to provide very precise and accurate measurement of the acceleration due to gravity. The basis of techniques used to measure acceleration due to gravity varies from using conventional mechanical methods, to manipulating cold atoms, to employing atomic interferometers. Although most of the aforementioned techniques can yield very accurate and precise measurement of the acceleration due to gravity, when using these techniques in introductory physics laboratory there are a few shortcomings.
This is due to the fact that these techniques require expensive experimental setups involving many components. Additionally, these techniques are difficult to perform and require near-ideal conditions to obtain reliable results. Last, but not the least, these techniques necessitate the hiring of highly-trained personnel. All these limitations can make the employment of these advanced techniques in teaching laboratories a difficult endeavor. The measurement of the acceleration due to gravity is now a standard teaching experiment in many introductory physics laboratory courses. Thus, most physics student labs desire an approach to measuring the acceleration due to gravity by using a method that is economical, simple, and safe, and which can also yield a reasonable value of a local acceleration of gravity g.
Of the many simple techniques employed to measure acceleration due to gravity in standard physics books, the period of a pendulum's oscillation and the time of fall of an object as a function of height are the most commonly used methods. While the pendulum, method can yield a relatively wide range of variation in the value of g due to effect of air resistance and other systematic errors, the latter method can also be very sensitive to imprecise measurements of times and heights of fall, consequently, causing significant variation in determining the value of g. In the last few decades, many experimental techniques have been proposed to replace these two simple methods to evaluate g. However, the application of these techniques was either deemed expensive or inaccurate, and sometimes unsafe.